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A318944 Number of Dyck paths with n nodes and altitude 4. 2
0, 0, 0, 0, 1, 8, 32, 114, 376, 1177, 3549, 10406, 29861, 84249, 234502, 645625, 1761765, 4772534, 12851261, 34434561, 91890118, 244385617, 648139821, 1714976054, 4529163125, 11942440233, 31448759302, 82727323369, 217426319541, 571033273142 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
REFERENCES
Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L. (2018). Enumerations of peaks and valleys on non-decreasing Dyck paths. Discrete Mathematics, 341(10), 2789-2807.
LINKS
FORMULA
a(n) = 9*a(n-1) - 31*a(n-2) + 50*a(n-3) - 36*a(n-4) + 8*a(n-5) for n>9. - Colin Barker, Apr 11 2019
MAPLE
(1-x)^2*x^4*(1+x-8*x^2+7*x^3)/(1-2*x)^3/(1-3*x+x^2) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ; # R. J. Mathar, Nov 25 2018
MATHEMATICA
LinearRecurrence[{9, -31, 50, -36, 8}, {0, 0, 0, 0, 1, 8, 32, 114, 376, 1177}, 30] (* Harvey P. Dale, Nov 03 2019 *)
PROG
(PARI) concat([0, 0, 0, 0], Vec(x^4*(1 - x)^2*(1 + x - 8*x^2 + 7*x^3) / ((1 - 2*x)^3*(1 - 3*x + x^2)) + O(x^40))) \\ Colin Barker, Apr 11 2019
CROSSREFS
A column of A318942.
Sequence in context: A204643 A036393 A003201 * A196097 A234272 A269077
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 18 2018
STATUS
approved

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Last modified April 16 07:08 EDT 2024. Contains 371698 sequences. (Running on oeis4.)